This invention relates to algorithms and devices for use in producing music. It is disclosed in the context of an instrument including a keyboard, but is believed to have utility for any other polyphonic instrument or in other applications as well.
For centuries musicians and mathematicians attempted to find a way of scaling a limited number of notes so that natural harmonics could be preserved, while melodies and harmonies were pitched at different levels, i.e., played in different keys. Many ways of tuning 12-note scales (12 notes per octave) were tried. All produced annoying dissonances and/or severely limited the keys (pitches) in which a piece could be played and the harmonic intervals which could be used. 13-note scales were tried (D# and E♭ were different notes) to provide more consonant intervals. Fourteen-note scales were also tried, and Handel even invented an instrument with a 70-note scale but could find noone who could play it. Finally, the compromise twelve tone, equal tempered scale was adopted. In this scale, all intervals except the octaves are dissonant, but music played in different keys retains the same interval relationships because the scale is a geometric progression. Even though this scale has now been in use for over two centuries, many musicians still find the dissonances produced by the scale to be annoying. String quartets eliminate some dissonances by tuning to each other, and find it difficult to play with pianos, which are generally tuned in equal tempered tuning. Likewise, the voices of barbershop quartets tune to each other, but almost always perform unaccompanied.
Several methods and apparatus are known which modify the equal tempered musical scale. There are, for example, the methods and apparatus described in U.S. Pat. Nos. 4,152,964; 4,248,119; 5,501,130; and, 5,736,661.
According an aspect of the invention, an instrument is provided which retunes itself in response to the chord being sustained and the way that chord is voiced.
According to another aspect of the invention, an instrument is provided which retunes itself in response to the chord being sustained and the separation of the notes in the chord.
According to another aspect of the invention, an instrument is provided which blends the notes of a chord the instrument is playing in view of the chord being sustained and its voicing.
According to another aspect of the invention, an instrument is provided which blends the notes of a chord the instrument is playing in view of the chord being sustained and the separation of the notes in the chord.
According to another aspect of the invention, an instrument is provided which retunes itself in view of the chord being sustained and the way talented musicians in ensembles tune to each other.
According to another aspect of the invention, a method is provided to develop alternative methods to retune the notes of a keyboard in view of the harmonics of contention, that is, harmonics that are separated typically by more than about one and one-half cents and less than about thirty-five cents apart, produced by the notes of the chord.
According to another aspect of the invention, a method is provided to produce consonant harmonics on a keyboard with equal tempered stretch tuning.
According to another aspect of the invention, a method is provided to obtain the consensus of experts as to the most desirable strategies for tuning different styles of music.
According to another aspect of the invention, a method is provided to obtain the consensus of experts as to the most desirable strategies for blending notes of a chord.
According to another aspect of the invention, a method is provided to obtain the consensus of experts as to the most desirable strategies for tuning in view of the kind(s) of ensemble(s) which is (are) performing (a) musical composition(s).
According to one aspect of the invention, a method of retuning a keyboard-type instrument starts from, and returns to, equal tempered stretch tuning based on the type of chord being sustained and the voicing of the chord.
According to another aspect of the invention, a method for generating harmonics for stretched tuning preserves consonance of harmonics.
According to yet another aspect of the invention, a method for retuning a keyboard type instrument is based on the chord type being played and the way the chord is voiced.
According to yet another aspect of the invention, a method is provided for determining which notes should be tuned as a sustained chord and which notes should be treated as passing notes.
According to yet another aspect of the invention, a method is provided for implementing options for how sustained chords can be retuned to eliminate dissonances and generate enhanced overtones.
According to yet another aspect of the invention, a method is provided for permitting musicians to select tuning strategies from combinations of options.
According to yet another aspect of the invention, a method is provided for retuning based on the chords, for example, 2-note chords, 3-note chords, 4-note chords, 5-note chords, created by the sustained notes.
According to yet another aspect of the invention, a method is provided for retuning based on the history of sustained notes.
According to yet another aspect of the invention, a method is provided for retuning based on tuning options as indicated by the setting of switches.
According to yet another aspect of the invention, a method is provided for tuning based on the length of time notes have been sustained and the interval positions they serve.
According to yet another aspect of the invention, a method is provided for starting from, and returning to equal tempered tuning based on the chord type being sustained, the voicing of the chord, and choices among options that have been made by experts.
According to yet another aspect of the invention, a method is provided for blending sustained chords so that no note stands out.
According to yet another aspect of the invention, a method is provided for retuning instruments so that they will closely approximate the way musicians and ensembles typically tune to each other.
According to an other aspect of the invention, a musical instrument includes a first switch having a first position in which the instrument is capable of producing tones, the intervals between which are equal tempered intervals of a twelve note octave. The first switch has a second position in which the instrument is capable of producing tones, the intervals between at least some of which are determined by identifying at least selected ones of the notes the instrument is being commanded to produce. The instrument also includes a processor including a map by which the identified notes are mapped to a chord type. The processor identifies a note in that chord type and substitutes a frequency closer to a harmonic of the identified note for the frequency of at least one harmonic of at least one other note the instrument is being commanded to produce.
Illustratively according to this aspect of the invention, the instrument includes a second switch. The processor includes at least two different maps. The second switch has a position for each map, permitting selection of one of the at least two different maps by which the instrument maps the identified intervals to a chord type.
Further illustratively according to this aspect of the invention, the instrument includes a third switch. The processor includes at least two different chord type decision engines. The third switch has a position for each chord type decision engine, permitting selection of one of the at least two different decision engines by which the instrument identifies a note of the chord type.
Additionally illustratively according to this aspect of the invention, the processor is a processor for substituting a frequency within a predetermined range of a harmonic of the identified note for the frequency of at least one harmonic of at least one other note the instrument is being commanded to produce.
Illustratively according to this aspect of the invention, the processor is a processor for substituting frequencies closer to at least two harmonics of the identified note for the frequencies of harmonics of at least two other notes the instrument is being commanded to produce.
Further illustratively according to this aspect of the invention, the processor is a processor for substituting frequencies closer to at least two harmonics of the identified note for the frequencies of at least two harmonics of at least one other note the instrument is being commanded to produce.
Additionally illustratively according to this aspect of the invention, the processor is a processor for permitting mapping of the identified notes to at least one of: a major triad; a minor triad; a triad suspended by a second; a triad suspended by a fourth; a major sixth; a minor sixth; a major seventh; a minor major seventh; a dominant seventh; a minor dominant seventh; a half diminished chord; a full diminished chord; and, an augmented chord.
Illustratively according to this aspect of the invention, the processor is a processor for resolving contention among competing ones of: a major triad; a minor triad; a triad suspended by a second; a triad suspended by a fourth; a major sixth; a minor sixth; a major seventh; a minor major seventh; a dominant seventh; a minor dominant seventh; a half diminished chord; a full diminished chord; and, an augmented chord, and mapping according to the contention resolution.
Further illustratively according to this aspect of the invention, the instrument includes a second switch. The processor includes at least two different chord type contention resolutions. The second switch has a position for each chord type contention resolution, permitting selection of one of the at least two different chord type contention resolutions by which the instrument identifies the chord type.
Additionally illustratively according to this aspect of the invention, the the processor is a processor for permitting mapping of the identified notes to an inversion of the chord.
Illustratively according to this aspect of the invention, the instrument includes a second switch. The processor includes a substitution decision engine. The second switch has a position in which the substitution decision engine is disabled and a position in which the substitution decision engine is enabled.
Further illustratively according to this aspect of the invention, the substitution decision engine has as an input at least one of: how long the instrument is commanded to sustain one of the twelve notes; the history of accumulated time of uninterrupted sustainment of a sustained note; the position a sustained note occupies in a chord; the position a sustained note occupied in a chord on at least one prior occasion; and, how much the note""s current assigned frequency varies from equal-tempered tuning.
Additionally illustratively according to this aspect of the invention, the the processor includes a lookup table by which the identified notes are mapped to a chord type, by which a note of the chord type is identified, and/or by which a frequency closer to a harmonic of the identified note is substituted for the frequency of at least one harmonic of at least one other note the instrument is being commanded to produce.
Illustratively according to this aspect of the invention, the instrument includes a keyboard having multiple keys for producing tones which are octaves of the at least one harmonic of the at least one other note the instrument is being commanded to produce. The processor substitutes octaves of the frequency closer to a harmonic of the identified note for the octaves of the frequency of at least one harmonic of the at least one other note the instrument is being commanded to produce.
Further illustratively according to this aspect of the invention, the processor includes a substitution decision engine having as an input how long the instrument is commanded to sustain one of the twelve notes. The processor reassigns the keys to producing tones which are octaves of the at least one harmonic of the at least one other note the instrument is being commanded to produce when the instrument is no longer commanded to sustain one of the twelve notes.
Additionally illustratively according to this aspect of the invention, the the processor is a processor for adjusting the amplitude of the frequency closer to a harmonic of the identified note which is substituted for the frequency of at least one harmonic of at least one other note the instrument is being commanded to produce.
Illustratively according to this aspect of the invention, the processor is a processor for adjusting the amplitudes of more than one of the tones the instrument produces in response to the commands to produce.
Further illustratively according to this aspect of the invention, the instrument includes a second switch. The processor includes at least two different amplitude decision engines. The second switch has a position for each amplitude decision engine, permitting selection of one of the at least two different amplitude engines by which the instrument adjusts the amplitudes of the tones.
According to another aspect of the invention, a musical instrument includes a first switch having a first position in which the instrument is capable of producing tones, the amplitudes of which are determined by identifying at least selected ones of the notes the instrument is being commanded to produce. The instrument further includes a processor including a map by which the identified notes are mapped to a chord type. The processor identifies a note in that chord type, and adjusts the amplitude of at least one of the tones the instrument produces in response to the commands to produce in response to the identified note.
Illustratively according to this aspect of the invention, the first switch has a second position in which the amplitude of the at least one tone the instrument produces in response to the commands to produce is not adjusted.
Further illustratively according to this aspect of the invention, the processor is a processor for adjusting the amplitudes of more than one of the tones the instrument produces in response to the commands to produce in response to the identified note when the first switch is in the first position.
According to another aspect of the invention, a method of operating a musical instrument capable of producing tones, the intervals between which are equal tempered intervals of a twelve note octave, and tones, the intervals between at least some of which are determined by identifying at least selected ones of the notes the instrument is being commanded to produce, includes identifying the at least selected ones of the notes the instrument is being commanded to produce, providing a map for mapping the identified notes to a chord type, identifying a note in that chord type, and substituting a frequency closer to a harmonic of the identified note for the frequency of at least one harmonic of at least one other note the instrument is being commanded to produce.
Illustratively according to this aspect of the invention, the method further includes providing at least two different maps, and selecting one of the at least two different maps by which the identified intervals are mapped to a chord type.
Further illustratively according to this aspect of the invention, the method includes providing at least two different chord type decision engines, and selecting one of the at least two different decision engines by which the instrument identifies a note of the chord type.
Illustratively according to this aspect of the invention, substituting a frequency closer to a harmonic of the identified note for the frequency of at least one harmonic of at least one other note the instrument is being commanded to produce includes substituting a frequency within a predetermined range of a harmonic of the identified note for the frequency of at least one harmonic of at least one other note the instrument is being commanded to produce.
Further illustratively according to this aspect of the invention, the method includes substituting frequencies closer to at least two harmonics of the identified note for the frequencies of harmonics of at least two other notes the instrument is being commanded to produce.
Additionally illustratively according to this aspect of the invention, the method includes substituting frequencies closer to at least two harmonics of the identified note for the frequencies of at least two harmonics of at least one other note the instrument is being commanded to produce.
Illustratively according to this aspect of the invention, providing a map for mapping the identified notes to a chord type includes providing a map for mapping the identified notes to at least one of a major triad, a minor triad, a triad suspended by a second, a triad suspended by a fourth, a major sixth, a minor sixth, a major seventh, minor major seventh, a dominant seventh, a minor dominant seventh, a half diminished chord, a full diminished chord, and an augmented chord.
Further illustratively according to this aspect of the invention, the method includes resolving contention among competing ones of a major triad, a minor triad, a triad suspended by a second, a triad suspended by a fourth, a major sixth, a minor sixth, a major seventh, a minor major seventh, a dominant seventh, a minor dominant seventh, a half diminished chord, a full diminished chord, and an augmented chord, and mapping according to the contention resolution.
Additionally illustratively according to this aspect of the invention, the method includes providing at least two different chord type contention resolutions, and permitting selection of one of the at least two different chord type contention resolutions by which the instrument identifies the chord type.
Illustratively according to this aspect of the invention, providing a map for mapping the identified notes to a chord type includes providing a map for mapping the identified notes to an inversion of the chord.
Further illustratively according to this aspect of the invention, the method includes providing a substitution decision engine, and selectively enabling the substitution decision engine.
Additionally illustratively according to this aspect of the invention, the method includes providing as an input at least one of: how long the instrument is commanded to sustain one of the twelve notes; the history of accumulated time of uninterrupted sustainment of a sustained note; the position a sustained note occupies in a chord; the position a sustained note occupied in a chord on at least one prior occasion; and how much the note""s current assigned frequency varies from equal-tempered tuning.
Illustratively according to this aspect of the invention, the method includes providing a lookup table by which the identified notes are mapped to a chord type, by which a note of the chord type is identified, and/or by which a frequency closer to a harmonic of the identified note is substituted for the frequency of at least one harmonic of at least one other note the instrument is being commanded to produce.
Illustratively according to this aspect of the invention, the instrument includes a keyboard having multiple keys for producing tones which are octaves of the at least one harmonic of the at least one other note the instrument is being commanded to produce. The method includes substituting octaves of the frequency closer to a harmonic of the identified note for the octaves of the frequency of at least one harmonic of the at least one other note the instrument is being commanded to produce.
Further illustratively according to this aspect of the invention, the method includes providing a substitution decision engine having as an input how long the instrument is commanded to sustain one of the twelve notes, and reassigning the keys to producing tones which are octaves of the at least one harmonic of the at least one other note the instrument is being commanded to produce when the instrument is no longer commanded to sustain one of the twelve notes.
Additionally illustratively according to this aspect of the invention, the method includes adjusting the amplitude of the frequency closer to a harmonic of the identified note which is substituted for the frequency of at least one harmonic of at least one other note the instrument is being commanded to produce.
Illustratively according to this aspect of the invention, the method includes providing at least two different amplitude decision engines, and selecting one of the at least two different amplitude engines by which the instrument adjusts the amplitude of the frequency.
Further illustratively according to this aspect of the invention, the method includes adjusting the amplitudes of more than one of the tones the instrument produces in response to the commands to produce.
According to another aspect of the invention, a method of operating a musical instrument capable of producing tones, the amplitudes of which are determined by identifying at least selected ones of the notes the instrument is being commanded to produce, includes providing a map by which the identified notes are mapped to a chord type, identifying a note in that chord type, and adjusting the amplitude of at least one of the tones the instrument produces in response to the commands to produce in response to the identified note.
Illustratively according to this aspect of the invention, the method includes selectively maintaining unadjusted the amplitude of the at least one tone the instrument produces in response to the commands to produce.
Further illustratively according to this aspect of the invention, the method includes adjusting the amplitudes of more than one of the tones the instrument produces in response to the commands to produce in response to the identified note when the first switch is in the first position.
According to another aspect of the invention, notes being played on a keyboard are classified into one of two categories: members of a sustained chord; or, passing notes.
A keyboard which incorporates the methods of this invention when used to accompany, or be a member of, an ensemble of tunable instruments, for example, bowed instruments such as violins and cellos, brass instruments, reed instruments, and human voices, will reduce clashes/inconsistencies between the harmonies the keyboard produces and those produced by the musicians who naturally tune to each other to reduce some of the most undesirable dissonances, generate brilliant overtones, and produce harmonies consistent with those produced by ensembles. When such an instrument is used to perform solos, it will produce music which is more pleasing because certain undesirable beat notes will be eliminated and the harmonies produced will be like those typically found by discriminating musicians to be more pleasing. Such an instrument uses an equal tempered scale as an underlying basis, as a point of departure and as a point of return.